Isospectral transformations between soliton-solutions of the Korteweg-de Vries equation

by Lee, Tad-ming

Abstract (Summary)

(Uncorrected OCR)
Absact of the entled
Isospectral Transformations etween Soliton-solutions of the orteweg-de
Vries Equation
Submitted by
Lee Tad Ming
for the Degree of Master of Philosophy
at The University of Hong Kong in March 1994.
Hee, he iosecl tanmas under he regime of superymmeic qan mechanic are employed to study special features ( main solto soluts ) of the eweg-de Vrie eq K-dV in t ). Such ransforma wih reference
to solto hery are ignificant becaus solton evolut are exactl sospecra s under he inver cattering me
The first pcedre to st sospecra Hamiltonian can e daed ack to
he wrk of Darbou 1882 and, er Cr 1955). Recently, he hery of su
erymmeric qantum mechanic in ne-dimenn has been developed and wide
died. One of the ide s of this they is to povide an n-hand ce
to stt the famiies of sospecra Hamiltonians. F his thery, a ecnd
of sospecral transforman was poposed Abraham and Moss (198). Puey
1986a) then inced a hird . A few year ag, Kng and Fung 1989 deve
oped a stemaic anas of the genera of ll thee isospecral transforma
nder a ing framewrk, mre ss long he ine of Sumar' rk ( Sumar
1985b ), adding ariculary an explicit treament of the ftright symmery They were abl to st ll transformas f he arboux-Cr crean and an-
nihi ransforma reing both regular and ingular solto potenials of the
K-dV eq
ccrding to the framewrk of ng and Fung 1989, an attempt wa made to
llustra he possble group poperies of the isospecral transforma which were
iniiaed Puey 1987) through 8 new oposs. Also vel st of acn-
ange variabl s poposed to mainain he ftright symmery of the isospecra
ransformas on eql footing. I bieve he acn-ange variabl give a mre suble decript of the Hamiltonian formul of the K-dV stem in cae we
have to hand bot he ft and he right scattering da
n addin, have generaized he addin ruls of regulari of the solto so luts of the K-dV eq nder he ransforma which were first repoed Wahst and Estoo 1973 in he en ha when successve ieras of the Backlund ransformas o he vacuu ste are applied to st t of N solto solut, can ovided he rul which help us to mainain he ingulari of the solut obtained
ii